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## Constructibility and Mathematical Existence

*Charles S. Chihara*

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ... More

## Mathematical Structuralism

*Charles S. Chihara*

### in Constructibility and Mathematical Existence

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) ... More

## Recent Attempts at Blunting the Indispensability Thesis

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The indispensability thesis maintains both that using mathematical terms and assertions is an indispensable part of scientific practice and that this practice commits science to mathematical objects ... More

## Grounding in Mathematical Structuralism

*John Wigglesworth*

### in Reality and its Structure: Essays in Fundamentality

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780198755630
- eISBN:
- 9780191816772
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198755630.003.0012
- Subject:
- Philosophy, Metaphysics/Epistemology

The grounding relation is thought to have certain structural properties: irreflexivity, asymmetry, transitivity, and well-foundedness. This paper examines a putative case of grounding that serves as ... More

## Categories for the Working Philosopher

*Elaine Landry (ed.)*

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198748991
- eISBN:
- 9780191811593
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198748991.001.0001
- Subject:
- Philosophy, History of Philosophy

Borrowing from the title of Saunders Mac Lane’s seminal work Categories for the Working Mathematician, this book aims to bring the concepts of category theory to philosophers working in areas ranging ... More

## Bicollective Ground: Towards a (Hyper)Graphic Account

*Jon Erling Litland*

### in Reality and its Structure: Essays in Fundamentality

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780198755630
- eISBN:
- 9780191816772
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198755630.003.0008
- Subject:
- Philosophy, Metaphysics/Epistemology

Grounding is bicollective if it is possible for some truths δ0, δ1, … to be grounded in the some truths γ0, γ1, …. without its being the case that each δi is grounded in some subcollection of ... More

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